A weighted mean (or weighted average) is like an ordinary mean, but the observations don't contribute equally - more emphasis is placed on some data values than others; they are weighted by a bigger or smaller amount than 1/n.

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152 views

Alternate weighting schemes for random effects meta-analysis: missing standard deviations

I am working on a random effects meta-analysis covering a number of studies which do not report standard deviations; all studies do report sample size. I do not believe it is possible to approximate ...
4
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1answer
372 views

Compare Log-Normal Distributions

I am looking at distributions for the fuel consumption of vehicles in the US and I have two sets of data: Data Set 1 - This is a dataset for the fuel consumption of all vehicles made available for ...
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1answer
62 views

Comparing retention rates with differing sample sizes

I'm looking to compare the retention rate of people who attended an event and those who did not. The list of those who did not (70) is significantly larger than those who have (28). Here is an ...
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1answer
21 views

Averaging and comparing mean values across studies

I am having a statistical problem that falls into two parts: (!) I have several literature reports on studies that have investigated the effect of drug "A" on a particular laboratory parameter. Some ...
0
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1answer
48 views

Permissible to use survey data in generating sampling weights?

Summary: Can I use non-population information (e.g. representative proportions from another survey) when calculating sampling weights? If so how might one account for the sampling error? I'm ...
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73 views

Weighting on tables

I have a question about terminology. Suppose I have data categorized by three factors A, B, and C, with cell means $\bar{y}_{ijk}$ and cell frequencies $n_{ijk}$, where $i$, $j$, and $k$ index A, B, ...
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69 views

Computation of the entropy of marginals?

I have implemented this paper: Efficient graph-based semi-supervised learning of structured tagging models In the last sentence of the section 4.2, the authors have mentioned another possible way of ...
2
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43 views

with two EWMA means of different window sizes, can we estimate any other means? slopes? jumps?

EWMA is defined as follows(1, 2, 3, 4, 5): $$ \mu_{N} = \frac {1}{N} \Sigma_{i=1}^{N}x_i $$ $$ =\frac {1}{N} \Sigma_{i=1}^{N-1}x_i + \frac{1}{N}x_{N} $$ $$ =\frac {N-1}{N} \frac{1}{N-1} ...
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155 views

Exponentially Weighing Moving Average (EWMA) for weekly data

I'm aware that the typical EWMA approach is applied over larger time periods (say for Volatility, where lambda = 94% and all weights add up to 100% for stock returns data from last 5 years). ...
2
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297 views

Weighted Standard Deviation vs. Weighted Regression Standard Error

This is an R question. I have $n$ observations of the variable $y$, with each observation, $i$, weighted by $w(i)$. Each $w(i)$ weight falls between zero and 1, with the sum of the weights, ...
2
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83 views

How to bootstrap confidence of a weighted measure?

I have a large data set of 20M observations with 20+ measures for each observation (people). Additionally I have a set of weights that reflect the racial population where each person lives. For ...
2
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0answers
32 views

Estimated Treatment Effect in the full sample is not between the estimates of the stratified samples?

I am estimating the relationship between students' math scores and using a supplemental math software. I've adjusted for some demographic variables in the model. In my first model, I use the full ...
2
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0answers
35 views

How to symmetrically adjust data by removing certain value

Say I have a data set in the following format: {a:200, b: 100; c:400} The sum of a, b and c equals 700. Now, I have another value which is supposed to be the actual total say 500. How do I adjust ...
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8 views

Constrained regression for binary dependent variable

I would like to discuss the methodology of the following case: I have a data for several patients over several years for 5 factors describing the health of a particular patient. Every factor consists ...
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11 views

Weighted sample mean and variance - asking for references and details

I found this wiki page which tells how to compute the weights to get a BLUE for the mean from correlated observation, assuming the correlation is known. What I'm asking is: Some references (books) ...
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42 views

Weighted arithmetic mean's alternative for ranking items

I have a Blog post ranking algorithm which has 5 factors which are considered for calculating final score. I have predefined input range according to which i decide score of a factor. e.g. Factor : ...
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19 views

Average Difference of Averages

I'm looking at the gender pay gap across the UK using some data from the ONS. The data is released as mean and median gross pay by sex by local authority area. Figures for England as a whole are also ...
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40 views

Gradient of a sum of indicators

EDITED w.r.t. whuber's comment: Say I have a function $\mathbb R^n \rightarrow \mathbb R$: $$f(w_1,\ldots,w_n) = \frac{n^-\sum_{i\in I^-}w_ix_i}{n^+\sum_{i\in I^+}w_ix_i}$$ with fixed $x_i\in\mathbb ...
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71 views

Okay to use oneway ANOVA to compare these 3 group proportions from aggregated dataset?

My situation: I am assessing outcomes of a university course redesign. One of the goals of the redesign project was to increase successful course completion, as measured by a decrease in the course ...
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56 views

Optimal weight for weighted average

I have some data points for which I do not have individual errors. My goal is to calculate the weighted average and I am looking for the "optimal weights" that can be used. I was thinking about the ...
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85 views

How did they do this analysis? (weighted proportions)

I've read with interest the report by Ayanian et al "Racial and Ethnic Disparities among Enrollees in Medicare Advantage Plans" [1]. They have estimated adjusted proportions of individuals that ...
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50 views

Mean of an interval censored random variable

It is likely that I am incorrect terminology here, but I am trying to compute a "mean" of an interval censored random variable. Here is an example where: 1. a random sample from the standard normal ...
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156 views

Aggregating Standard Errors for Predicted Probability Estimates

I obtain predicted values from a logistic regression for a certain outcome (e.g., mortality) at the hospital level – the data is at the patient level – and need to compute the average across ...
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130 views

Weighted variance of the weighted variance in frequency transition matrix?

Assume I have a $m\times n$ Transition Matrix $A$ with $m$ different observations and $n$ represents a discrete state space. Each column counts the frequency that state $j\in [1...n]$ was visited from ...
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31 views

Computationally cheap estimation of the mode from 2D samples

I say 'mode' in the title – perhaps there's something more appropriate I can find. Here's my problem: A person is in a $100\mathrm m$ by $500\mathrm m$ space. I have about 100 samples randomly ...
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37 views

Aggregating based on inverse probability weight

I have a data set that includes life quality indices for many cities. I want to aggregate the indices to the metropolitan level. Since some cities in each metro area are missing, the data set provides ...
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50 views

How do I determine the appropriate “weight” of a point in fantasy basketball?

For fantasy basketball, I want to quantify a player's output based on his Points, Rebounds, Assists, Steals, 3s, and Blocks production. Let's pretend that over the course of an imaginary basketball ...
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175 views

Hypothesis test for difference between domain means with weighted data

I have a large dataset that is weighted due to: probability proportional to size sampling, & disproportionate stratification. I would like to compare the means for two different domains ...
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0answers
12 views

How to introduce a weighted percentage?

We wanted to know the knowledge of people about how to eat fruits. For this we provided a party and invited 1000 people. There were 3 kind of fruits on the tables. Banana, orange and melon. If ...
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32 views

P-values of weighted means and weighted standard deviations

I have a lot of data like this: control: 0/12 0/14 0/12 and case: 104/111 94/108 36/57 and when I use arithmetic means and unbiased sample variance, I get mean1 = 0.000000 mean2=0.816049 ...
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6 views

How does PSPP handle weighting

In an answer to a related question regarding the statistical program SPSS it is stated that the program handles weighting just by repeating an observation x times (where x is the weighting factor). ...
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27 views

Calculating the Title odds

Given a set of expected values within an event. How do you calculate the probability of each of them occuring the most? i.e. Who will win the league? total goals scored in a season , given expected ...
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27 views

Estimating variance or coefficient of variation for population given total and count for four segments of population

My goal is to estimate the coefficient of variation for a population, but the data we have been given is very limited. All we have is the total and count for four segments of the population. The ...
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8 views

Time weighted variables

anyone please help... Variables: *Independent variable: BP in followup *Dependent variable: Change in Glucose/year (ordinal: low:<-10/year, moderate: -10/year to 10/year, high: >10/year) Time: ...
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23 views

Sampling distribution of the *weighted* mean

I'm wondering if someone could send me a book reference about the sampling distribution of the weighted mean, I have found some information in wikipedia, however, I'm needing a more complete and ...
0
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0answers
12 views

Is there a way to calculated weighted mean with two weights associated with each value?

If there are n values with 2 weights w1 and w2 associated with each, is there a way to use both w1 and w2 to calculate the weighted mean?
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46 views

Calculating a cubic mean value which summarizes conditions with different probabilities

I am not sure how to calculate a 'typical' cubic mean load (CML, where L=load=force) given CML values for various conditions which have different probabilities of occurrence. The conditions are ...
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60 views

Hypothesis test for 2 Weighted Means

I was trying to compare pairs of medical cost from several customized groups. The medical cost is adjusted by age and gender distribution in the sample. The resulting per member medical cost in each ...
0
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0answers
21 views

Comparing weighted means of unequal subsets of values

If I have a range of data on a grid with associated weights, what is a correct method of calculating a weighted mean of values that fall within one cell, so they may be compared with the weighted ...
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124 views

Ranking based on weight for multiple variables and objectives

First of all, I know very little about statistics. I need help ranking a set of multiple solutions (about 138 solutions) based on three objectives. I work on the architectural design field, I analyzed ...
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41 views
0
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46 views

Estimate the population variance from a set of weighted means

Proviso: I do not have a lot of experience with statistical theory, so please forgive my occasionally poor choice of notation.$$\\$$ My problem is as follows: I have a set of measurements $X_i, ...
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106 views

Averaging standard deviations of unequal weight?

I'm sorry if the title is unclear, but I'm not sure of the appropriate way to phrase this question. I'm in med school (and sadly not as versed in statistics as I ought to be), and I am trying to use ...
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0answers
48 views

Construct confidence interval for price per area, from weighted average price for quantity, and weighted average quantity per area

I have function for obtaining the weighted mean for price per quantity, where $p$ is price, and $w$ is the weight, for some product $i$. $$\bar p_a = \sum p_{i} w_{i}$$ and a quantity per area, ...
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179 views

Standard Error for Relative Frequency Distribution

I have a weighted distribution with weights $w_i$, such that: $$\sum_i{{w_i}}=1$$ I know that the mean is defined by: $$\sum_i{{w_i}{x_i}}=\mu$$ And that the unbiased variance is defined as: ...
0
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0answers
209 views

Borda Count (Weighted Sum) vs Weighted Mean

I recently ran a survey where I gave users 36 options and had them rank their top 10 from most important to least important. I've taken the results and assigned each position a weight (i.e. ranked ...
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181 views

Identification of Difference in Weighted Mean and its Standard Error in Clustered Data Using Stata

I already asked this question on the statalist but have not received any comments on this issue yet. So I am going to post it here too. I am concerned with the following problem. Suppose my data ...
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34 views

Do I need to use weighted means with the Wilcoxon signed rank test?

I have 22 patients. They have been measured pre and post treatment. There are 3 measurements per patient before treatment (pre baseline), and four measurements after treatment (post baseline). There ...
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0answers
137 views

Best fit of weighted mean?

The title might be somewhat misleading. I am trying to solve the following optimization problem and do not find any clues. Can any one help? I have a sequence of $n$ observation $s_i$. Each ...
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0answers
112 views

Weighting datapoints by uncertainty - asymmetric CIs

I have several estimates obtained using different softwares, these programs give me an estimate as well as a 95% confidence interval. However, these CIs are not symmetric around my point estimates, ...